Question

A man buys a plot of land at 3,60,000. He sells one third of the plot at a loss of 20%.Again he sells two third of the plot left at profit of 25%At what price should he sell the remaining plot in order to gain 10% on the whole transaction ?

Answer 1

Cost of plot = Rs 3,60,000 (C)

Target sale value to achieve 10% profit on the whole plot = 360000 + (360000 x 0.1) = Rs 396000 (T)

Cost of 1/3 plot = 360000 ÷ 3 = Rs 120000 (c1)
Cost of 2/3 plot = 360000 - 120000 = Rs 240000
Cost of 2/3 plot of 2/3 (plot left after selling 1/3 plot) = 240000 x (2 ÷ 3) = Rs 160000 (c2)

20% loss amount on sale of 1/3 plot = 120000 x 0.2 = Rs 24000
Sale price of 1/3 plot = a - 24000 = Rs 96000 (s1)

Remaining plot is 2/3
Man sells 2/3 of this 2/3 plot at a profit of 25% = 160000 x 0.25 = Rs 40000
Sale price of 2/3 of 2/3 plot = 160000 + 40000 = Rs 200000 (s2)

Total sale value realized so far R = s1 + s2 = 96000 + 200000 = Rs 296000
Target sale value to achieve 10% profit on the whole plot = S (calculated above)
∴ Required sale price for the remaining plot = S - R
= 396000 - 296000
= Rs 100000

Answer 2

Cost =  Rs 3, 60, 000.

cost of 1/3 of the plot = Rs 1,20,000.
loss due to its sale = 20% = Rs 24,000.

cost of the second 1/3 of the plot = Rs 1,20,000
Profit due to its sale = 25% = Rs 30,000.

Net profit to be gained on the overall sales = 10%  =  Rs 36, 000. 
  
Profit to be gained from the sale of third part = Rs 36,000 - 30, 000 + 24,000
       = Rs 30,000 

So Sale price for the last 1/3 of the plot = Rs 1,20, 000 + Rs 30, 000
       = Rs 1, 50, 000.